Steve Roth uses the phrase “savings” as a stock. Obviously his claim is just wrong as we know from national accounts:

Change in net worth = Saving + Holding Gains.

(with netting in holding gains).

Steve Keen doesn’t use saving as a stock but as a flow and a plural of saving. But Steve Keen’s point is also wrong. National saving is equal to the sum of saving of all economic units, such as households, firms, government etc. Even the household sector’s propensity to save collectively matters. That’s what macroeconomics is all about.

Now moving the more important point: is it possible that a higher propensity to consume reduces the long run rate of accumulation?

There are several Post-Keynesian economists who have considered the possibility. Of course it should be contrasted with supply side neoclassical economics. A few are Basil Moore, Wynne Godley, Marc Lavoie, and Gérard Duménil and Dominique Lévy as mentioned at the beginning of this post.

We quickly discovered that the model could be run on the basis of two stable regimes. In the first regime, the investment function reacts less to a change in the valuation ratio-Tobin’s q ratio-than it does to a change in the rate of utilization. In the second regime, the coefficient of the q ratio in the investment function is larger than that of the rate of utilization (γ3 > γ4). The two regimes yield a large number of identical results, but when these results differ, the results of the first regime seem more intuitively acceptable than those of the second regime. For this reason, we shall call the first regime a normal regime, whereas the second regime will be known as the puzzling regime. The first regime also seems to be more in line with the empirical results of Ndikumana (1999) and Semmler and Franke (1996), who find very small values for the coefficient of the q ratio in their investment functions, that is, their empirical results are more in line with the investment coefficients underlying the normal regime.

… In the puzzling regime, the paradox of savings does not hold. The faster rate of accumulation initially encountered is followed by a floundering rate, due to the strong negative effect of the falling q ratio on the investment function. The turnaround in the investment sector also leads to a turnaround in the rate of utilization of capacity. All of this leads to a new steady-state rate of accumulation, which is lower than the rate existing just before the propensity to consume was increased. Thus, in the puzzling regime, although the economy follows Keynesian or Kaleckian behavior in the short-period, long-period results are in line with those obtained in classical models or in neoclassical models of endogenous growth: the higher propensity to consume is associated with a slower rate of accumulation in the steady state. In the puzzling regime, by refusing to save, households have the ability over the long period to undo the short-period investment decisions of entrepreneurs (Moore, 1973). On the basis of the puzzling regime, it would thus be right to say, as Dumenil and Levy (1999) claim, that one can be a Keynesian in the short period, but that one must hold classical views in the long period.

So there is a possibility that a higher propensity to consume leads to a lower growth in the long run. I do not think this is generally true, but this could be possible in some economies.

Two conclusions. It’s counter-productive to mix the definition of saving and what’s called “net lending” in national accounts. It’s possible (which shouldn’t mean that it’s necessarily the case) that Keynes’ paradox of savings doesn’t hold in the long run. I don’t believe that’s the case but purely arguing using national accounts and/or changing definitions won’t do.

This is an updated version of a post whose link has been removed and the content added below.

The world is more Kaldorian than Keynesian. After the crisis, Keynes became popular again but his Cambridge descendent Nicholas Kaldor is hardly remembered by the economics community. Even his biographers have some memory loss of him.

😉

Anthony Thirlwall and John E. King are biographers of Nicholas Kaldor. Superb books.

There’s a chapter Talking About Kaldor: An Interview With John King in Anthony Thirlwall’s book Essays on Keynesian and Kaldorian Economics. There’s an interesting discussion on money endogeneity (Google Books link):

J.E.K. … I wonder if Kaldor would have gone as far as Moore in arguing that the money supply curve is horizontal.

Anthony Thirlwall replies saying he would have argued that the supply of money is elastic with respect to demand, instead of quoting him. Here’s Nicholas Kaldor stating explicitly in a footnote in Keynesian Economics After Fifty Years, in the book, Keynes And The Modern World, ed. George David Norman Worswick and James Anthony Trevithick, Cambridge University Press, 1983, on page 36:

Diagrammatically, the difference in the presentation of the supply and demand for money, is that in the original version, (with M exogenous) the supply of money is represented by a vertical line, in the new version by a horizontal line, or a set of horizontal lines, representing different stances of monetary policy.

[italics: mine]

Anthony Thirlwall is one of the commenter in the book chapter. The book is proceedings of a conference on Keynes.

But that’s not enough. Turn to page 363 of the book.

A.P.T. He had a very high regard for Sraffa but he never wrote on this topic.

J.E.K. Not something that would really have concerned him very much? Too abstract and too removed from reality?

A.P.T. Probably, yes. It is quite interesting that Sraffa was his closest friend, both personal and intellectual, and they used to meet very regularly – almost every day when Sraffa was alive. But there’s no evidence that they ever discussed Production of Commodities by Means of Commodities.

J.E.K. That’s amazing. There’s certainly no evidence that he ever wrote anything on those questions.

A.P.T. There’s no evidence that he wrote anything, or that indeed he really understood Sraffa. Well, he had the broad thrust, but I don’t know that he ever read it carefully, or understood the implications.

In Volume 9, of Kaldor’s Collected Works, there are two memoirs. One of Piero Sraffa and the other on John von Neumann.

The Federal Reserve produces quarterly data for the financial accounts of the United States (earlier called “flow of funds”). There are a few notable additions termed enhanced financial accounts, which are in the process of being added. Some additions are details about money market mutual funds, off-balance sheet items of depository institutions, such as unused commitments, letters of credit and derivatives. This is the chart from the Federal Reserve’s FEDS note Off-Balance Sheet Items of Depository Institutions in the Enhanced Financial Accounts

This data is probably not new but has been added in the report. Indeed it was one of the important points of Basil Moore’s book Horizontalists and Verticalists.

Moore has a sophisticated way of saying things (pages 24-25):

In making a loan commitment a bank should be viewed as a participant in forward rather than spot lending markets. Viewed as a seller of contingent claims, banks themselves obviously can excercise only limited control over the volume of their lending.

On page 186 of Moore’s book, he also notes that Keynes talks about this in his book A Treatise On Money:

Keynes insists that cash facilities of the public includes unused overdraft facilities, “of which we have no statistical record whatever” (JMK, 5, p. 37). He then concludes, “Thus the cash facilities, which are truly cash for the purposes of the theory of the value of money, by no means correspond to the bank deposits which are published” (JMK, 5, p. 38).

Keynes then returned to the issue of unused overdraft facilities, without, however, recognizing that this was the key to the endogeneity of the money stock:

[Keynes]: In Great Britain the banks pay great attention to the amount of their outstanding loans and deposits, but not to the amount of their customers’ overdraft faclities … it means that there is no effective pressure on the resources of the banking system until the finance is employed … there is no superimposed pressure resulting for planned activity over and above the pressure resulting from actual activity. (JMK, 14, pp. 222-23).

Honestly, I am not sure what Keynes is trying to say in all this. Moore is quite clear in his book. It’s still nice to know that Keynes discussed all this. Perhaps he wanted to say something more but couldn’t translate his thoughts in words. But if you can interpret Keynes, do tell me!

It is interesting that the recent Bank of England quarterly bulletin referred to an article of Peter Howells, a Post-Keynesian (also available here), although I don’t think the authors appreciate why the paper is interesting.

The title of my blog post is flicked from a paper by Basil Moore which is in reply to Howells.

Howells sets up the problem:

[B]anks set up their collateral standard and lending rates … and then meet all loan requests forthcoming. The demand for loans is determined by other variables in the economic system … making the loan volume exogenous from the banks’ point of view and the resulting quantity of deposits endogenous … Notice, crucially that in this view, increases in the money supply are demand-determined but the demand in question is the demand for loans … the question then is what reconciles the demand resulting from this lending with peoples’ willingness to hold money? … What is it that ensures that the supply of new deposits created by the flow of net new lending is just equal to the quantity demanded?

Let me present it in another way. To be clear let us assume the economy is closed. Output is determined by domestic demand or by private expenditure and government expenditure. Output is equal to the national income and is distributed to various economic units such as households who among other things allocate a part of their wealth into deposits. So there is a money demand. Of course expenditure is partly from income and sale of existing assets and by borrowing from other economic units and in particular from banks which lend by creating deposits in this process. So there is a change in the money supply. So there are two pictures with overlapping stories but not exactly so the question is – what processes ensure that

Ms = Md

is valid at every instant of time?

Does the rise in income and higher demand for money (because of a rise in wealth) alone ensure this? Is there a price clearance? Prices of what? Goods and services? Or prices in financial markets? (‘price’ includes interest rates such as deposit rates, loan rates, bond yields, equity prices and so on).

Also note this is in nominal variables. So is the rise in income purely due to a rise in prices or purely a rise in real output or a mix of the two? What causes inflation?

Where does QE fit into this? Does it raise output? Real/nominal? Raise prices – of goods and services or asset prices or both?

It is important to appreciate the formulation of the question. In case you don’t yet appreciate the question, more from Howells:

The starting point is that the demand for the loans that create the deposits originates in the desire of deficit units to spend in exceess of income. It is a question of financing an income-expenditure discrepancy. Furthermore, it is a decision made by a subset of the community since not everyone is involved in demanding an increase in their indebtedness to banks. (Indeed it is not even the case that everyone holds a stock of bank debt…). By contrast, the decision to hold (i.e., not spend) the newly created deposits is a portfolio decision. Furthermore, it is a decision made by different people (“the community as a whole”) from those concerned with borrowing it… the fact remains that so long as we are dealing with two groups of agents, with different motives, an ex ante coincidence of preferences is quite implausible. The question, then, is how are these ex ante preferences to be reconciled, ex post.

… Howells considers four responses that have been proposed to his conundrum:

Kaldor and Trevithic[k] – any excess money is automatically extinguished as a result of the repayment of bank debt.

Chick – the income multiplier process will automatically increase the demand for active balances.

Laidler – the buffer stock demand for money is a demand “on average” over a period of time, rather than a demand for a fixed stock at a moment of time.

Moore – “convenience lending,” the rejection of an independent money demand curve, rooted in a “full-blooded rejection of the idea of equilibrium”: In a non-ergodic world, no meaning can be attached to the notion of a unique general equilibrium stock of money demanded.

Howells maintains that the above list offers “promising solutions” to the mechanism that reconciles net new lending to borrowers with the change in the demand for money for the wealth holders. But he concludes that “each … on its own is almost insufficient” for the “reconciliation. As a result, he proposes that variations in relative interest rates, “which can and do occur continuously, provide the key to the fine-tuning required by the balance-sheet identity” …

Frequently in such discussions the accommodative behaviour of the banking system is forgotten. So there is another mechanism as highlighted by Nicholas Kaldor in his book The Scourge Of Monetarism (Oxford University Press, 1982):

As it is, a highly developed banking system already provides such facilities on an ample scale, since it is prepared to accommodate the public’s changing demand between different types or financial assets by altering the composition of the banks’ assets or liabilities in a reverse direction. If the non-banking public wishes to switch its holding of gilts for interest-bearing bank deposits, the banks are ready to supply such deposits at the minimum of inconvenience, and at the same time to place their surplus funds into the gilts which were previously held by the public. Similarly the banks provide easy facilities to their customers for switching balances on current accounts into interest-bearing deposit accounts, or vice versa.

In general banks not only hold government bonds but also other kinds of securities such as mortgage-backed securities, agency debt and so on. In olden days, there was no securitization and banks would hold more government bonds which got substituted. (See the Fed’s H.8 weekly release for data on banks’ assets) [There’s a Geithner ppt which mentions this in one slide, anyone has a link?]

This point is an important one because here the reconciliation happens via changes in quantities. Remember it is not just loans which create deposits but also banks buying bonds from the non-banking system which create deposits.

The answers to these questions can be found systematically by using James Tobin’s asset allocation theory.

Let me mention some positions. At one end are Monetarists for whom the direction of causality is from money to other things. So there may be an excess of money and if so leads to higher expenditure and a hot potato process in which money supply and demand are brought into equivalence by rise in prices of goods and services. It can also lead to a rise in real output but the Monetarists emphasize the price aspect more. In addition they also distinguish between government expenditure and private expenditure and try to point out that the latter is more efficient and so on.

Looking at an economy as a moving picture, as expenditures increase, output rises and there is a rise in prices of goods and services and a rise in the stock of money. Monetarists look at coincident events and assign some strange causalities.

Moving beyond Monetarism, there’s also a view that the reconciliation of the supply and demand for money necessarily happens via a rise in interest rates on everything including bank loans leading to a crisis. Of course that it not true because beyond a point banks will reduce lending instead of offering loans at higher interest rates. Banks have their own animal spirits but this is via tightening credit standards, quality of collateral etc. Also this is not the only outcome because the process of lending and borrowing increases output and income and can stabilize debt ratios. Nonetheless, debts can move into unsustainable territories and financial crisis do happen, and when it happens, there’s a high demand for money and the reconciliation may happen via bankruptcies of firms and the central bank may need to accommodate the rise in demand for money by lending at a large scale since bankruptcies threaten a fall in output.

Of course there are many more mechanisms for the reconciliation which I have avoided. It may happen that due to changes in portfolio preferences, there is a stock market boom and firms will go IPO instead of borrowing from the banking system. So we have economic units who wish to hold less money and more equities and firms borrowing less from the banking system leading to a reconciliation. (A more careful analysis is needed because firms have deposits after having raised funds through an IPO).

Now consider convenience lending. There is of course some truth to it. If you receive you salary on a Friday evening, you are not rushing to allocate newly held deposits into the stock market because it is already closed (unless you have an international brokerage account). So you are holding the deposits non-volitionally. However, subscribing to convenience lending alone is a bit extreme.

Now to QE/LSAP. When the central bank purchases financial assets such as government bonds from the markets, it creates bank settlement balances and deposits in the process. Wealth holders will then purchase other assets and the reconciliation happens via changes in prices of financial assets.

This post is far from any complete analysis of the interesting questions but hopefully I have got readers interested in something. The question on reconciliation asks what reconciliates the demand and supply of money – income, prices (of goods and services or prices in financial markets), quantities and so on. Also, some seem to think that “price clearing” has to do with some notions about an equilibrium. I don’t think these two are the same things. One can have price changes and clearances without appealing to the notion of any “equilibrium”.

In the natural sciences, controversies are settled in a few months, or at a time of crisis, in a year or two, but in the social so-called sciences, absurd misunderstandings can continue for sixty or a hundred years without being cleared up.

– Joan Robinson, 1981 (1979), What Are The Questions And Other Essays – Further Contributions To Modern Economics, M.E. Sharpe

The latest Bank of England Quarterly Bulletin (2014 Q1) will be released on the 14th. It has pre-released two articles which go into money creation and the myths associated with it.

The page is here. The second article Money creation in the modern economymay interest you more but the first is also readable.

Interestingly, the second pape refers to Post-Keynesians : Tom Palley’s 1996 book , Basil Moore’s 1988 book, a JPKE paper by Peter Howells and a 1981 paper by Nicholas Kaldor and J. Trevithick which discusses the reflux mechanism (reprinted in Kaldor’s Collected Economic Essays, Vol. 9). It also refers to James Tobin’s 1963 paper Commercial Banks As Creators Of “Money”.

One negative is the omission of fiscal policy from the discussion altogether and emphasising monetary policy. This underplay of fiscal policy and overemphasis of monetary policy is one deep bias of the profession. The paper also has a slightly different emphasis on what determines the quantity of lending than emphasized by Post-Keynesians but I won’t go into it now. Still the page is worth a look.

Louis-Philippe Rochon and Sergio Rossi have a very interesting articleEndogenous Money: The Evolutionary Versus Revolutionary Views in the Review Of Keynesian Economics. I think it was written many years back and was in an unpublished form and has been published now. It is a nice critique of views of some Post-Keynesians such as Victoria Chick and also others such as Basil Moore. For instance, the paper quotes Moore’s view from 2001:

[w]hen money was a commodity, such as gold, with an inelastic supply, the total quantity of money in existence could realistically be viewed as exogenous.

Click the image to visit the ROKE website.

There are also some nice articles in a recent issue of JPKE on neoliberalism and the financial crisis.

Some gossip: The JPKE was initially supposed to have been called Journal of Keynesian Economics but it didn’t make it because the acronym would have been JOKE.

Also, Jayati Ghosh has written an excellent blog article on Thatcherism – the ‘triumph of private gain over social good’ (borrowing words from her).

Matias Vernengo has a recent blog post on the persistence of poverty in the United States. Which reminds me of an interview clip of Anwar Shaikh titled “The Sin Of Our Era”:

Back to formal matters.

What does it mean when an economist says words such as “endogenous”, “exogenous”? Most of the times, economists – mainstream economists – themselves confuse these terms and hence you see a lot of usage of these words in Post-Keynesian economics.

An exogenous variable is supposed to be a causal variable, if the structure of a model has economic meaning. In fact, it is usually just a variable that is put on the right-hand side of equations in a model, but not on the left-hand side.

Similarly, an endogenous variable is supposed to be a caused variable. In fact, it is usually just a variable that shows up at least once on the left-hand side of an equation

Apparently no generally accepted concept of an endogenous money stock (or monetary base) has been defined. In statistical theory a variable is endogenous if it is jointly determined with other variables in the system. However, many monetary theorists have chosen to call a variable endogenous only if its magnitude is not under the control of policymakers. Such semantic problems have undoubtedly prolonged this debate.

For the money stock measure such as M1, M2 etc., there shouldn’t be any confusion. The trouble arises for things such as interest rates. For example, some economists may say that if inflation rises, the central bank may/will raise the short-term interest rate and it is endogenous while others will say it is up to the central bank to decide how much to change the interest rate, if at all. Such things lead to a lot of debate.

I like the latter usage (the control sense) but I think it is difficult to exclusively have the same usage.

The word “control” is also misunderstood. Here is a fine article on Wynne Godley in The Times from 16 June 1978 where he details on how misunderstood the word is:

There was a discussion last week on a social network site on Basil Moore’s book Horizontalists And Verticalists. Someone mentioned he never knew anyone who owned a copy of the book! Lucky me.

I was browsing through my copy and came across this – which I thought I should quote on central bank “defensive behaviour”.

Actually, among Post-Keynesians, Alfred Eichner was the first to understand and highlight the “defensive” nature of central bank open market operations.

Outside PKE, it was a paper of Raymond E. Lombra and Raymond G. Torto titled Federal Reserve Defensive Behaviour And The Reverse Causation Argument which started analyzing the details of the Federal Reserve defensive behaviour and supported the theory of endogenous money on which economists such as James Tobin and Nicholas Kaldor were writing at the time. The term “defensive” was coined by Robert Roosa of the Federal Reserve in the bookFederal Reserve Operations In The Money And Government Securities Markets originally written in 1956.

Recently central banks around the world have been doing a lot of things (“unconventional measures”) in trying to “boost” their economies – such as “large scale asset purchases” (QE). For some, recent central bank action is the natural way to start to understand monetary economics. For me, it is first important to understand what they did before the crisis to correctly understand what they have been doing and judge if their actions have any usefulness at all – on a case by case basis.

Anyways, here is from Basil Moore’s book (pages 97-99):

Open-market operations: defensive rather than dynamic?

According to the conventional story taught in most textbooks and worked through by students in countless T-account exercises, central bank open-market security purchases have expansionary effects on the money stock by raising the high-powered base. Central bank security sales conversely lower the high-powered base, and so operate to reduce the stock of money outstanding.

Table 5.2 presents the relationship between changes in total bank reserves, the monetary base, and the Federal Reserve net open-market security purchases or sales. The data are monthly time intervals for the period October 1979 to December 1983. This is the period when quantitative targeting was purportedly at last rigorously instituted. Nonborrowed reserves were avowedly the Fed’s chief operating instrument for controlling the growth rate of the monetary aggregates.

To the student of introductory economics, and even to many economists, these results will surely be startling. On a monthly basis, Federal Reserve net open-market operations fail to explain any of the actual changes in unadjusted or adjusted total reserves! They explain only 5 percent of changes in the unadjusted and only 10 percent of the changes in the high-powered base. In all cases the coefficient on net open-market purchases and sales is extremely small. It has no statistical significance in explaining observed changes in bank reserves. Although the coefficient is statistically significant in explaining the monetary base, its magnitude implies that $1000 of open-market purchases or sales were necessary to change the value of the base by $1!

The explanation for these apparently puzzling results is not far to seek (Lombra and Torto, 1973). From the central bank’s point of view a large number of stochastic nonpolicy factors operate to add or withdraw reserves from the banking system. These factors can be analyzed by an examination of the central bank’s balance sheet identity. This documents the various financial flows that accompany any change in the base: changes in float, changes in the public’s currency holding, foreign capital inflows or outflows, changes in treasury balances held with the Fed, changes in bank borrowing from the discount window. All of these flows are completely outside the control of the monetary authorities. In order to achieve a desired level of the base, these flows must be completely offset by open-market operations.

If the Fed were to take no action in the face of these large stochastic inflows and outflows of funds, the banking system would experience sharp fluctuations in its excess reserve position. Such changes would be unrelated to the Federal Reserve’s policy intentions, and would provoke continued liquidity crises and great instability in interest rates. As a result most Federal Reserve open-market operations are “defensive” and designed to offset the effects of these nonpolicy forces. Central banks operate to make reserves available to the banking system on reasonably stable terms, from day to day and week to week.

Studies of Federal Reserve open-market operations have estimated that more than 85 per cent of Federal Reserve security purchases of [sic] sales are “defensive” (Lombra and Torto, 1973, Forman, Groves and Eichner, 1984). Such flexibility is needed to deal with the very large inherent volatility of money flows. On a week-to-week basis such “noise” in the behaviour of the narrow money supply accounts for dollar changes in reserves of plus or minus $3 billion more than two-thirds of the time. This represents nearly 10 percent of total reserves, which were concurrently in the order of $40 billion (J. Pierce, 1982). On a monthly bias, such “noise” accounts for changes in the money stock or plus or minus 5 percent about two-thirds of the time.

The accounting identities equating aggregate expenditures to production and of both to incomes at market prices are inescapable, no matter which variety of Keynesian or classical economics you espouse. I tell students that respect for identities is the first piece of wisdom that distinguishes economists from others who expiate on economics. The second?… Identities say nothing about causation.

Let us look at their basic model which still has income not equal to expenditure. Now whichever way one presents it (with better defined terms using phrases “ex-ante”, “ex-post”, “planned”, “unplanned”, one cannot escape the conclusion income = expenditure).

The model is below – found on page 15.

Keen has a simple two-sector model of households and production firms and it can also be thought of as a three sector model where production firms borrow from banks to finance investments.

In the last equation, you see Keen and Grasselli’s claim that expenditure is income plus change in debt.

The trouble is with Keen’s behavioural assumption (1.4)

C = W + ΠD

Unfortunately the rules of accounting do not allow this!

If the assumption (1.4) is relaxed, firms’ increase in debt is mirrored by households’ saving.

In a three sector model with households, firms and banks, the increase in firms’ debt is mirrored as increase in households’ deposits.

It can be generalized with firms issuing some securities purchased by households.

So equation 1.8 should read:

YE = YI

with no need of Lebesgue Integrals to prove (1.8) is correct because it is not correct.

The Saving = Investment Identity

The Keen-Grasselli model doesn’t respect the identity

Saving = Investment

This can be easily seen. Households (in his language workers) having zero saving and zero investment. Firms have a saving of ΠR and investment of I.

So total saving = ΠR and total investment = I

But because these terms differ by ΔD (equation 1.5), they cannot be equal unless ΔD = 0.

So in the Keen-Grasselli model,

Saving ≠ Investment

The reason Keen and Grasselli get this inconsistency is because they assume that saving is volitional.

Basil Moore was aware of this and in his book Shaking The Invisible Hand, he wrote:

The belief that aggregate saving is the sum of volitional saving decisions by individual economic units is simply a spectacular macroeconomic illustration of the “fallacy of composition.” This fallacy has been reinforced by the unfortunate use of the colloquial verb “to save,” with its very powerful transitive volitional connotations, for an economic term which is merely an intransitive accounting definition: “income not consumed.” As economists know, it is a “fallacy of composition” that what is true for the part is necessarily also true for the whole. Total “saving” is the sum of total saving undertaken by individual “savers.” But since saving is the accounting record of investment it cannot be the sum of volitional individual saving decisions. Aggregate saving is not the sum of individual savers volitional decisions to save. It follows that in all monetary economies most “saving” is “non-volitional.”

[emphasis: mine]

Ideally (i.e., realistically) Keen’s model should sit inside a model with the government and the government would end up running surpluses. Non-volitonally 🙂 S = I would be maintained and so would YE = YI

Some Higher Mathematics: The Dirac Delta Function

Keen and Grasselli claim that confusions around economists being not able to see things in continuous time is the source of errors by them and that the reason is that debt injections are sudden.

Now, in calculus, there is a thing called the Dirac Delta Function.

[Paul Dirac didn’t get the media attention that Einstein got but he was surely his equivalent. The Delta function is just a small contribution when compared to what he did elsewhere. He was Feynman’s hero.]

The delta function δ(x) is zero at all points except 0 where it is infinite. But the integral of δ(x) from over the range of real numbers is 1. That is difficult to digest initially when first tries to learn it.

A debt injection is a step function jump in debt. The delta function has a curious property that it is the derivative of the step function.

So income flows can be represented as sum of delta functions which different coefficients at different points in time.

So Keen’s chart (Figure 13) in his paper should have income represented as delta function spikes.

To get the flow over a period, one has to integrate and this will result in the income over the period to be the sum of the coefficients of these delta functions.

So whether in discrete formulation or continuous time formulation, YE = YI for the whole economy and the reason is not hard to guess because dD/dt cancels out with dA/dt since assets and liabilities are created equally.

For an individual sector it is true that YE = YI + dD/dt – nobody disagrees with that but to be more accurate the right hand side should include minus dA/dt.

Also, a continuous time formulation is just taking infinitesimal intervals and then treating infinite of them together.

It makes no sense to say income before debt injection was $100 for real world transactions in a continuous time formulation. It is actually zero just before a debt injection because all income/expenditure flows are “spikey”.

Just after the debt injection it is zero again because nobody spends the instant a loan is given. The debt injection increases assets and liabilities by the amount of the loan if the borrowing is from a bank.

So after the loan is given at the next infinitesimal, change in debt is zero and income/expenditure is also zero.

Then income/expenditure flow spikes at the moment the transaction happens – like a delta function.

But that is income for someone and for an economy as a whole Income = Expenditure.

Anyway, nothing of the analysis justifies the definition of “aggregate demand” (now renamed by Keen to “effective demand”).

The central message of this book is that members of the economics profession, all the way from professors to students, are currently operating with a basically incorrect paradigm of the way modern banking systems operate and of the causal connection between wages, prices, on the one hand, and monetary developments, on the other. Currently, the standard paradigm, especially among economists in the United States, treats the central bank as determining the money base and thence the money stock. The growth of the money supply is held to be the main force determining the rate of growth of money income, wages, and prices.

… This book argues that the above order of causation should be reversed. Changes in wages and employment largely determine the demand for bank loans, which in turn determine the rate of growth of the money stock. Central banks have no alternative but to accept this course of events, their only option being to vary the short-term rate of interest at which they supply liquidity to the banking system on demand. Commercial banks are now in a position to supply whatever volume of credit to the economy their borrowers demand.

The book built on his own work and that of Nicholas Kaldor and Marc Lavoie among others goes on to describe the banking system, horizontalism and endogenous money. Money is credit-led and demand-determined was his message. Economists believing in the “incorrect paradigm” are Verticalists in Moore’s terminology.

Paul Krugman whom Post Keynesian have more respect than other mainstream economists probably disappointed them when he was arguing with Steve Keen in a 3-post blog series. Arguing like a Verticalist, Krugman claims (among other Verticalist claims) in his post Banking Mysticism, Continued:

… And currency is in limited supply — with the limit set by Fed decisions. So there is in fact no automatic process by which an increase in bank loans produces a sufficient rise in deposits to back those loans, and a key limiting factor in the size of bank balance sheets is the amount of monetary base the Fed creates — even if banks hold no reserves.

The Defensive Nature Of Open Market Operations

The reason there is widespread misunderstanding of what the central bank does is because it carries out open market operations where it buys or sells government securities or does repurchase agreements. The orthodox view is that the central bank is acting the way it is to increase or decrease the amount of banks’ settlement balances and this affects the money supply – allowing banks to expand lending or leading them to contract – and thence the whole economy. The view is that the central bank has a direct control these operations and are purely volitional.

This is an incorrect view because no central bank claims to be “controlling” the money stock.

If money is truly endogenous, the question is why the central bank does these operations often. The reason is that operations of the central bank are defensive.

In his article Endogenous Money: Accomodationist, Marc Lavoie argues:

Some post-Keynesians have pointed out long ago that open market operations had little or nothing to do with monetary policy.

For instance, It is usually assumed that a change in the Fed’s holdings of government securities will lead to a change, with the same sign attached, in the reserves of the commercial banking system. It was the failure to observe this relationship empirically which led us, in constructing the monetary financial block of our model, to try to find some other way of representing the effect of the Fed’s open market operations on the banking system. (Eichner, 1986, p. 100)

That other way is that ‘the Fed’s purchases or sales of government securities are intended primarily to offset the flows into or out of the domestic monetary-financial system’ (Eichner, 1987, p. 849).

So the central bank purchases government bonds and/or does repos to neutralize the effects of transactions which change the settlement balances. One example is the flow of funds into and out of the government’s account at the central bank. Another is the demand for currency notes by banks to satisfy their customers’ needs. The central bank has no choice but to provide these notes.

Krugman is partly right when he says, “Banks are important, but they don’t take us into an alternative economic universe.” However he fails to see that money is endogenous and the way the banking system works show this endogeneity.

Of course, Steve Keen has issues with his models and accounting with which Krugman has troubles. Keen defines aggregate demand to be gdp plus “change in debt”. As much weird this definition is, it is double counting when investment expenditure is financed by borrowing rather than internal sources of funds. Also, if a person sells a home to another person who has financed this purchase by borrowing and the former does not make expenditure from this income, this does not increase aggregate demand – a point raised by Marc Lavoie here (h/t “Circuit” from Fictional Reserve Barking). But as per Keen’s definition it does. In his first post, Krugman seems to say the same thing as Lavoie – but in a roundabout way.

The resulting debate has however highlighted the Verticalist intuition of Krugman!

Some of the previous posts went into the economic concept of Private Saving and Private Saving Net of Investment. For a closed economy these are:

Private Saving = Private Investment + Budget Deficit

Private Saving Net of Investment = Budget Deficit

For an open economy, we add the current balance of payments to the right of both these equations.

So we have the sectoral balances identity:

NPS = DEF + CAB

for Net Private Saving or Saving Net of Investment. Confusingly, Net Saving is used to mean Saving Net of Consumption of Fixed Capital. Consumption of fixed capital is the national accounting equivalent of depreciation but since there is a different accounting treatment, the former phrase is used.

In addition to Investment by the private sector, there’s also public investment and we need a bookkeeping concept of National Saving.

Just like we consolidated the domestic private sector into one, we could also consolidate the whole nation for specific purposes.

First take a closed economy. Since Income = Expenditure and Saving is defined so that consumption and investment expenditures are treated differently, we have

Gross Saving = Gross Domestic Investment

To get Net Saving, one has to subtract consumption of fixed capital from both sides.

Economies however are open. Hence we need to modify the above equation. Simultaneously taking depreciation into account, we have:

Remember this Net Saving is different from the other usage which is Saving Net of Investment.

Before verifying that this is indeed the case for the United States, it is worth mentioning that the difference between saving and surplus (or financial balance) applies to the government sector as well. The following is from the Table F.8 of the Z.1 Flow of Funds Accounts of the United States.

(click to expand and click again to expand)

So in green – for the year 2001 for the United States – you see both the gross saving and saving net of consumption of fixed capital of the government sector is positive whereas the government’s budget balance is in deficit.

This shouldn’t be surprising given we saw the same for the private sector.

Back to national saving, we can verify the identity. The current balance of payments is a nation’s income minus expenditure (only in a closed economy, these two are equal). If this is positive, the nation as a whole has a positive net lending. Else, it is a net borrower.

The identity can be seen using the numbers circled in red (and including the statistical discepancy).

The Paradox Of Thrift

The analysis above can mislead one into believing that since “saving” is a positive word, the nation as a whole should save by whatever means – such as by inducing the household sector to increase its propensity to save or aiming for a balanced budget (or worse, aiming to retire the public debt).

Both ideas are vacuous. A spontaneous increase in the propensity to save works by reducing the output and a tight fiscal stance achieves the same i.e., reducing the national saving or private saving as a whichever is the case – as a result of lower demand and output.

The Loanable Funds Fallacy

The simple accounting relations are also used in economics textbooks to promote saving in general because due to the above identity, one can be fooled into believing that a higher saving leads to higher investment. Again such ideas are promoted in public debates to argue against higher government expenditure and to even promote making balanced budget constitutional! The story goes that higher saving allows more investment because supposedly there are more funds to lend for investment.

This is based on the incorrect notion of the exogeneity of money. While this cannot be discussed in a single post, it’s where ideas of endogenous money and Horizontalism are illuminating.

Basil Moore had an article titled Saving Is The Accounting Record Of Investment, where he discusses some of the points here – never mind his claim that “total saving on an economy cannot reflect the volitional behavior of savers”. Here’s a Google Books preview from his book Shaking The Invisible Hand:

Mercantilism

The Mercantilists observe the accounting identity about national saving and the fact that it is related to the balance of payments and conclude that foreign trade is highly important in the growth of nations and hence well being and quality of life. The connection is that saving achieved via running a trade surplus with the rest of the world increases a nation’s net worth. To promote less consumption, the same mantra of national saving is used. So it is related to the paradox of thrift.

These ideas are used in public discussions on the problem of the external sector imbalance whether one believes in Mercantilism or not (their idea of rejection of the invisible hand). An increase in the household propensity to save (achieved by whatever means) or an attempt to reduce the budget balance by a tighter fiscal stance improves the current account balance, only because it results in a lower domestic demand and output and hence higher unemployment – all undesirable. That of course does not mean that one can unilaterally relax fiscal policy but just points to a more international effort needed badly right now to solve the problem of global imbalances.

While there is some truth to Mercantilists’ view, it’s for slightly different reasons – it is advantageous so some in one sense and injures others and hence inures everyone in the end.

In the General Theory Keynes introduced open economy considerations in his discussion of Mercantilism. He argued that the Mercantilists had been correct in their belief that a favorable balance of trade was desirable for a country, since increases in foreign investment increase domestic AD exactly like increases in domestic investment:

When a country is growing in wealth somewhat rapidly, the further progress of this happy state of affairs is liable to be interrupted, in conditions of laissez-faire, by the insufficiency of the inducements to new investment. … the well-being of a progressive state essentially depends … on the sufficiency of such inducements. They may be found either in home investment or foreign investment … which between them make up aggregate investment. … The opportunities for home investment will be governed in the long run by the domestic rate of interest; whilst the volume of foreign investment is necessarily determined by the size of the favourable balance of trade. …

Mercantilist thought never supposed that there was a self-adjusting tendency by which the rate of interest would be established at the appropriate level…

In a society where there is no question of direct investment under the aegis of public authority,… it is reasonable for the government to be preoccupied … [with] the domestic interest rate and the balance of foreign trade. … when nations permit free movement of funds across national boundaries the authorities have no direct control over the domestic rate of interest or the other inducements to home investment, measures to increase the favourable balance of trade [are] the only direct means at their disposal for increasing foreign investment; and, at the same time, the effect of a favourable balance of trade on the influx of precious metals was their only indirect means of reducing the domestic rate of interest, and so increasing the inducement to home investment.

Keynes emphasized that any domestic employment advantage gained by export-led growth was a zero-sum game and “was liable to involve an equal disadvantage to some other country.” He argued that export-led growth aggravates the unemployment problem for the surplus nation’s trading partners, who are forced to engage in “an immoderate policy that (may) lead to a senseless international competition for a favourable balance, which injures all alike.” The traditional approach to improve the trade balance has been to attempt to make the domestic export and import-competing industries more competitive, either by forcing down nominal wages to reduce domestic production costs, or by devaluing the exchange rate. Keynes argued that gaining competitive gains by reducing nominal price variables would tend indirectly to foster a state of global recession. One’s trading partners would be forced to attempt to regain their competitive edge by instituting their own restrictive policies. When nations fail jointly to undertake expansionary policies to raise domestic investment and generate domestic full employment, free international monetary flows create a global environment where each nation has national advantages in a policy of export-led growth. The pursuit of these policies will lead to a race to the bottom, that “injures all alike.”

the weight of my criticism is directed against the inadequacy of the theoretical foundations of the laissez-faire foundations upon which I was brought up and which for many years I taught—against the notion that the rate of interest and the volume of investment are self-adjusting at the optimum level, so that preoccupation with the balance of trade is a waste of time.

These apposite warnings of Keynes have gone virtually unnoticed as mainstream economists have waxed enthusiastic about the benefits of liberalized financial markets and the export-led economic miracles of the Asian “Tigers,” and now the miracle of China. Modern economies have become more open than when Keynes was writing, so it is imperative that Keynes’ open economy analysis becomes better known.